Number worksheet — GCSE Higher

1.Write down the symbol that makes this statement true: −2/3 ___ −5/6

2.A window display has red baubles, gold baubles and green baubles in the ratio 4 : 5 : 6. What fraction of the baubles are not green?

3.The recurring decimal 0.454545... can be written as 0.45 recurring, where both digits repeat forever. Let x = 0.45 recurring. Work out x as a fraction in its simplest form.

4.Work out 3 × (−2)² − 5

5.Tickets for a fairground ride are sold in packs of 6. Tokens for the dodgems are sold in packs of 10. Yusuf wants to buy the smallest number of packs of each so that he ends up with the same number of ride tickets as dodgem tokens. Work out how many ride tickets that is.

6.A water tank holds 80 litres when full. It currently contains 60 litres. Work out what fraction of the tank is empty.

7.Simplify ⁴√(16a⁸b¹²)

8.Leah measures the length of her classroom with a tape measure marked in centimetres. She writes the length down as 7.3157 m. Give a reason why this is not an appropriate degree of accuracy.

9.Work out 3 + 4 × (−2).

10.An allotment plot is divided into vegetables and flowers in the ratio 9 : 4. A third of the vegetable section is used for potatoes. What fraction of the whole plot is potatoes?

11.A jug holds 3 1/3 litres of juice. Each glass holds 2/3 of a litre. Work out how many glasses can be filled from the jug.

12.Expand and simplify √3(2 + √12).

13.Work out the exact value of √(2² + 3²)

14.Maya buys 4 plants at £3.20 each and a bag of compost for £6.75. She pays with a £20 note. Work out her change.

15.A roll of ribbon is 8.4 m long. Ribbon is cut into pieces that are each 0.6 m long. Work out how many complete pieces can be cut from the roll.